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A081278 Binomial transform of Chebyshev polynomial coefficients A001793. 3
1, 6, 29, 126, 513, 1998, 7533, 27702, 99873, 354294, 1240029, 4290894, 14703201, 49955454, 168466797, 564390342, 1879706817, 6227425638, 20533285917, 67411165086, 220442258241, 718277586606, 2332658764269, 7552375012566 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-27,27).

FORMULA

a(n) = (n^2+8*n+9)3^(n-2).

a(n) = 9*a(n-1)-27*a(n-2)+27*a(n-3) for n>2, a(0)=1, a(1)=6, a(2)=29. [Corrected by Paolo P. Lava, Jun 16 2008]

G.f.: (1-2*x)*(1-x)/(1-3x)^3.

MATHEMATICA

CoefficientList[Series[(1 - 2 x) (1 - x) / (1 - 3 x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 07 2013 *)

PROG

(MAGMA) [(n^2+8*n+9)*3^(n-2): n in [0..25]]; // Vincenzo Librandi, Aug 07 2013

CROSSREFS

Cf. A007051, A006234, A081279.

Sequence in context: A243474 A111644 A225618 * A054146 A172062 A081674

Adjacent sequences:  A081275 A081276 A081277 * A081279 A081280 A081281

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 16 2003

STATUS

approved

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Last modified October 21 06:25 EDT 2019. Contains 328292 sequences. (Running on oeis4.)